Linear Algebra Examples

$100000 = (C F) (\frac{1 - ({(\frac{1}{1.0075})}^{360})}{0.0075})$

Step 1

Since $C$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$C F (\frac{1 - {(\frac{1}{1.0075})}^{360}}{0.0075}) = 100000$

Step 2

Simplify.

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Step 2.1

Divide $1$ by $1.0075$ .

$C F \frac{1 - {0.99255583}^{360}}{0.0075} = 100000$

Step 2.2

Raise $0.99255583$ to the power of $360$ .

$C F \frac{1 - 1 \cdot 0.067886}{0.0075} = 100000$

Step 2.3

Multiply $- 1$ by $0.067886$ .

$C F \frac{1 - 0.067886}{0.0075} = 100000$

Step 2.4

Subtract $0.067886$ from $1$ .

$C F \frac{0.93211399}{0.0075} = 100000$

Step 2.5

Divide $0.93211399$ by $0.0075$ .

$C F \cdot 124.28186567 = 100000$

Step 3

Divide each term in $C F \cdot 124.28186567 = 100000$ by $F \cdot 124.28186567$ and simplify.

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Step 3.1

Divide each term in $C F \cdot 124.28186567 = 100000$ by $F \cdot 124.28186567$ .

$\frac{C F \cdot 124.28186567}{F \cdot 124.28186567} = \frac{100000}{F \cdot 124.28186567}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $F$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{C F \cdot 124.28186567}{F \cdot 124.28186567} = \frac{100000}{F \cdot 124.28186567}$

Step 3.2.1.2

Rewrite the expression.

$\frac{C \cdot 124.28186567}{124.28186567} = \frac{100000}{F \cdot 124.28186567}$

Step 3.2.2

Cancel the common factor of $124.28186567$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{C \cdot 124.28186567}{124.28186567} = \frac{100000}{F \cdot 124.28186567}$

Step 3.2.2.2

Divide $C$ by $1$ .

$C = \frac{100000}{F \cdot 124.28186567}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move $124.28186567$ to the left of $F$ .

$C = \frac{100000}{124.28186567 \cdot F}$

Step 3.3.2

Factor $100000$ out of $100000$ .

$C = \frac{100000 (1)}{124.28186567 \cdot F}$

Step 3.3.3

Factor $124.28186567$ out of $124.28186567 \cdot F$ .

$C = \frac{100000 (1)}{124.28186567 (F)}$

Step 3.3.4

Separate fractions.

$C = \frac{100000}{124.28186567} \cdot \frac{1}{F}$

Step 3.3.5

Divide $100000$ by $124.28186567$ .

$C = 804.62261694 \frac{1}{F}$

Step 3.3.6

Combine $804.62261694$ and $\frac{1}{F}$ .

$C = \frac{804.62261694}{F}$

Step 4

Set the denominator in $\frac{804.62261694}{F}$ equal to $0$ to find where the expression is undefined.

$F = 0$

Step 5

The domain is all values of $F$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${F | F \neq 0}$

Step 6